Mathematical analysis of the Mandelstam-Tamm time-energy uncertainty principle

In the Mandelstam-Tamm version of the time-energy uncertainty principle Delta t denotes the infimum of time intervals that elapse before the change in the mean of any observable has the same magnitude as its standard deviation. We clarify this interpretation, and show that the infimum is achieved for certain observables and thus that this famous inequality is actually an equality. (C) 2005 American Institute of Physics.